Final answer:
To solve the quadratic equation 2x^2 + 11x + 128 = 0 in factored form, we need to find two binomials that, when multiplied together, equal the original expression. None of the given factored forms are correct.
Step-by-step explanation:
To solve the quadratic equation 2x^2 + 11x + 128 = 0 in factored form, we need to find two binomials that, when multiplied together, equal the original expression. We can start by factoring out the common factor of 2:
2(x^2 + 5.5x + 64) = 0
Next, we need to find two binomials that can be multiplied together to give us x^2 + 5.5x + 64. Using the quadratic formula, we can find the roots of this quadratic equation:
x = (-5.5 ± √(5.5^2 - 4(1)(64)))/(2(1))
After simplifying the expression, we get:
x = (-5.5 ± √(30.25 - 256))/2
x = (-5.5 ± √(-225.75))/2
The square root of a negative number is not a real number, so this equation has no real roots. Therefore, none of the given factored forms (a), b), c), or d)) are correct.